• 대한수학회보
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• 제45권4호
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• pp.607-614
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• 2008

We present coincidence points and common fixed point results for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature.

• 대한수학회지
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• 제33권4호
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• pp.709-716
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• 1996

Nielsen coincidence theory is concerned with the determinatin of a lower bound of the minimal number MC[f,g] of coincidence points for all maps in the homotopy class of a given map (f,g) : X $\to$ Y. The Nielsen Nielsen number $N_R(f,g)$ (similar to [9]) is introduced in [3], which is a lower bound for the number of coincidence points in the relative homotopy class of (f,g) and $N_R(f,g) \geq N(f,g)$.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.279-308
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• 2021

The purpose of this paper is to introduce a class of contractive pairs of mappings satisfying a Zamfirescu-type inequality, but controlled with altering distance functions and with parameters satisfying the so-called Geraghty condition in the framework of b-metric spaces. For this class of mappings we prove the existence of points of coincidence, the convergence and stability of the Jungck, Jungck-Mann and Jungck-Ishikawa iterative processes and the existence and uniqueness of its common fixed points.

• 충청수학회지
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• 제15권1호
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• pp.1-6
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• 2002

David Gavid [3] proved that in many familiar cases the upper semi-finite topology on the set of closed subsets of a space is the largest topology making the coincidence function continuous, when the collection of functions is given the graph topology. Considering G-spaces and taking the coincidence set to consist of points where orbits coincidence, we obtain G-version of many of his results.

• 충청수학회지
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• 제28권1호
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• pp.13-28
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• 2015

In this paper, we use two mappings satisfying certain expansive conditions to construct convergent sequences in complex valued metric spaces, and then we prove that the limits of the convergent sequences are the points of coincidence or common fixed points for the two mappings. The main theorems in this paper are the generalizations and improvements of the corresponding results in real metric spaces, cone metric spaces and topological vector space-valued cone metric spaces.

• East Asian mathematical journal
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• 제32권5호
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• pp.701-716
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• 2016

We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.

• 대한수학회지
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• 제35권1호
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• pp.165-175
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• 1998

We give a generalization of the selection theorem of Ben-El-Mechaiekh and Oudadess to complete LD-metric spaces with the aid of the notion of n-connectedness. Our new selection theorem is used to obtain new results of fixed points and coincidence points for compact lower semicontinuous set-valued maps with closed values consisting of D-sets in a complete LD-metric space.

• 대한수학회보
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• 제33권2호
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• pp.205-211
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• 1996

Throughout this paper, we will work in the category of compact connected manifolds and continuous maps. If $X_1, X_2$ are manifolds, $f, g: X_1 \to X_2$ are maps, then a point $x \in X_1$ is a coincidence of f and g iff f(x) = g(x) ; the set of all such points is denoted by Coin(f,g).

• Korean Journal of Mathematics
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• 제15권1호
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• pp.39-49
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• 2007

A few existence results of nonunique coincidence points for some kinds of $\acute{C}$iri$\acute{c}$ type mappings in metric and pseudocompact Tichonov spaces, respectively, are proved. The results presented in this paper extend some known results in the literature.

• 대한수학회지
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• 제32권2호
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• pp.171-181
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• 1995

Nielsen coincidence theory is concerned with the estimation of a lower bound for the number of coincidences of two maps $f,g: X \longrightarrow Y$. For this purpose the so-called Nielsen number N(f,g) is introduced, which is a lower bound for the number of coincidences ([1]). The relative Nielsen number N(f : X,A) in the fixed point theory is introduced in [3], which is a lower bound for the number of fixed points for all maps in the relative homotopy class of f:(X,A) $\longrightarrow$ (X,A), and its estimation is given in [5].